The tan( Command

Command Summary

Returns the tangent of a real number.

Command Syntax

tan(angle)

Press TAN

TI-83/84/+/SE

1 byte

tan(θ) calculates the tangent of the angle θ, which is defined by $\tan \theta=\frac{\sin \theta}{\cos \theta}$

The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle*180/π and from degrees to radians is angle*π/180. The tan( command also works on a list of real numbers.

Since tangent is defined as the quotient of sine divided by cosine, it is undefined for any angle such that cos(θ)=0.

tan(π/4)
1


In degrees:

tan(45)
1


You can bypass the mode setting by using the ° (degree) and r (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

tan(45°)
1

tan(π/4¹ )
1


# Error Conditions

• ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
• ERR:DOMAIN is thrown if you supply an angle of π/2±nπ (in radians, where n is an integer) or 90±180n (in degrees, where n is an integer), or when the input is ≥1E12.

.